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Multi-Part Lesson 1
Get ConnectED
Measures of Central TendencyAPART B C D E F
Multi-Part Lesson 1
650 Analyze Data and Graphs
Median, Mode, and Range HURRICANES The table
shows the number of Atlantic
hurricanes in different years.
1. Order the data from least to
greatest. Which piece of data
is in the middle of this list?
2. Compare this number to the
mean of the data.
A data set can also be described by its median or its mode. The mean,
median, and mode are called measures of central tendency because
they describe the center of a set of data.
Median and Mode
The median is the middle number of the ordered data or the mean of the middle two numbers.
The mode is the number or numbers that occur most often.
Find the Median and the Mode
MONKEYS The table shows the Number of Monkeys
28 36 18 25 12 44 18 42 34 16 30
number of monkeys at eleven
different zoos. Find the median
and mode of the data.
Order the data from least to greatest.
Median 12, 16, 18, 18, 25, 28, 30, 34, 36, 42, 44 28 is in the middle.
Mode 12, 16, 18, 18, 25, 28, 30, 34, 36, 42, 44 18 occurs most often.
The median is 28 monkeys. The mode is 18 monkeys.
a. BUILDINGS The list shows the number of stories in the
11 tallest buildings in Springfield. Find the median and
mode of the data.
40, 38, 40, 37, 33, 30, 20, 24, 21, 17, 19
Main IdeaFind and interpret the median, mode, and range of a set of data.
Vocabularymeasures of central
tendencymedianmoderange
Vm
Atlantic Hurricanes
5 15 9 7 4 9 8
The range of a set of data is the difference between the greatest and
the least values of the set. A large range indicates that the data are
spread out. A small range indicates that the data are close in value.
Find the Range
COINS The table gives
the weights and
diameters of the coins
used in the U.S. Find
the range of the
weights. Then write
a sentence that
describes how the
data vary.
The greatest weight is 5.670 grams, and the least weight is
2.268 grams. So, the range is 5.670 - 2.268 or 3.402. The range
is relatively large, so the data are spread out.
b. COINS Find the range of the diameters of the coins above. Then
write a sentence that describes how the data vary.
WEATHER Find the mean, median,
mode, and range of the temperatures
displayed in the graph.
Mean 64.4 + 71.2 + 55.8 + 58.2
__ 4
= 249.6 _
4 or 62.4°
Median 55.8, 58.2, 64.4, 71.2
58.2 + 64.4
_ 2 = 122.6
_ 2
= 61.3°
Mode There is no mode.
Range 71.2 - 55.8 = 15.4°
c. BACKPACKS Find the mean, Cost of Backpacks ($)
16.78 48.75 31.42 18.38
22.89 51.25 28.54 26.79
median, mode, and range
of the costs in the table.
Coin Weight (g) Diameter (mm)
dime 2.268 17.91 nickel 5.000 21.21 penny 2.500 19.05 quarter 5.670 24.26
United States Coins
Wed.Tue.Mon.Sun.
6065
55
050
7570
Tem
pera
ture
(°F)
Day
64.4
71.2
55.8 58.2
Daily High Temperature
There are an even number of data values. So, to find the median, find the mean ofthe two middle numbers.
Everyday Use
Range in music, all the notes between the high and low notes, as with a singer with a wide range
Math Use
Range the difference between the greatest number and least number in a set of data
Range The range of a set of data describes how much the data vary. It is called a measure of variability.
Lesson 1D Measures of Central Tendency 651
Find the median, mode, and range for each set of data.Examples 1 and 2
1. points scored by football team: 15, 20, 23, 13, 17, 21, 17
2. monthly spending: $46, $62, $63, $57, $50, $42, $56, $40
Find the mean, median, mode, and range of the data represented.Example 3
3. 4.Cost of CDs ($)
11.95 12.89 19.99
19.99 12.59 18.49
20102009200820072006
3020
010M
embe
rs
4050
Year
21 19
40
26
14
Debate Club Membership
= Step-by-Step Solutions begin on page R1. Extra Practice begins on page EP2.
Find the median, mode, and range for each set of data.Examples 1 and 2
5. age of employees: 23, 22, 15, 36, 44
6. minutes spent on homework: 18, 20, 22, 11, 19, 18, 18
77 math test scores: 97, 85, 92, 86
8. height of trees in feet: 23, 27, 24, 26, 26, 24, 26, 24
ANALYZE DISPLAYS Find the mean, median, mode, and range of the data
represented. Round to the nearest tenth if necessary.
Example 3
9. 10.Average Speeds (mph)
40 52 44 46
52 40 44 50
41 44 44 50
Test Grades
100 77 80 65
87 85 85 82
100 97 95 75
11. 12.
1 2 3 4 5 6 7
2
4
6
8
Laps
Sw
am
10
1214
16
Day
0
Emilia’s Swimming Schedule
Num
ber o
f Job
s
05
1015202530
Month321 4 5 6
813 12
26
1510
Yardwork Jobs
B 1313 ANALYZE TABLES A Louisville Daily High Temperatures (°F)
Louisville Lexington
75 50 80 72 80 73 75 74
70 84 70 71 76 76
newspaper claims that during seven
days, the high temperature in
Lexington was typically 6° warmer
than the high temperature in
Louisville. What measure was used to
make this claim? Justify your answer.
14. MATH IN THE MEDIA Use the Internet to find the high temperatures for
each of the last seven days in a city near you. Then find the median high
temperature.
15. GRAPHIC NOVEL Refer to the graphic novel frame below for Exercises a–b.
Let’s check
other measures
to really see
which team is
better.
a. Find the median, mode, and range for each team’s wins.
b. Which team had the better record? Justify your response.
C 16. CHALLENGE The ticket prices for a concert series were $12, $37, $45,
$18, $8, $25, and $18. What was the ticket price of the eighth and
final concert in this series if the set of 8 prices had a mean of $23,
a mode of $18, a median of $19.50, and a range of $37?
17. REASONING One evening at a local pizzeria, the following number of
toppings were ordered on each large pizza.
3, 0, 1, 1, 2, 5, 4, 3, 1, 0, 0, 1, 1, 2, 2, 3, 6, 4, 3, 2, 0, 2, 1, 3
Determine whether each statement is true or false. Explain your
reasoning.
a. The greatest number of people ordered a pizza with 1 topping.
b. Half the customers ordered pizzas with 3 or more toppings,
and half the customers ordered pizzas with less than 3 toppings.
18. E WRITE MATH In the data set {3, 7, 4, 2, 31, 5, 4}, which measure
best describes the set of data: mean, median, or mode? Explain your
reasoning.
Lesson 1D Measures of Central Tendency 653
Test PracticeT
23. CELL PHONE Find the mean number of cell phone minutes Tucker
used each month this year. (Lesson 1B)
Month Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.
Minutes Used 49 65 20 37 55 68 75 50 24 37 42 30
24. Malcolm’s and Leo’s last four math test scores are shown in the graphs
below. Write a sentence comparing the mean scores of the students. (Lesson 1B)
19. EXTENDED The Quest
Year Number of Concerts
2003 142
2004 142
2005 136
2006 136
2007 124
2008 138
2009 136
2010 150
RESPONSE The
table shows the
number of concerts
performed by The
Quest.
Part A What is the difference between the median number of concerts and the mode number of concerts for 2003–2010?
Part B Write a sentence describing the data.
20. The lengths of the 5 long jumps at track
practice were 14.5 feet, 13.7 feet, 14.1 feet,
14.9 feet, and 13.8 feet. What would the
sixth length have to be to have a mean
length of 14.1 feet?
A. 14.8 feet C. 13.6 feet
B. 14.1 feet D. 12.9 feet
21. SHORT RESPONSE The prices of some
dinners at the Town Diner are shown in
the table.
Dinner Price($)
Turkey 9.90
Cheeseburger 6.75
Chicken Salad 5.29
Spaghetti 8.15
What is the range of prices in dollars for
the meals?
22. The table shows the number of schools
in 12 different counties. What is the
median of the data?
Number of Schools
4 3 6 10 3 148 5 7 11 7 8
F. 4 H. 7
G. 6 I. 8
Malcolm’s Test Scores
1 2 3 4
Test
Scor
e (p
erce
nt)
0
20
40
60
80
100 78%88% 90%
100%Leo’s Test Scores
1 2 3 4
Test
Scor
e (p
erce
nt)
0
20
40
60
80
100 80% 78%92% 94%